Sex-specific differences in the growth and population characteristics of Sand crab Ovalipes punctatus (De Haan, 1833) in coastal waters of Korea

The sex-specific differences in the growth and population characteristics of the high-commercial-value sand crab Ovalipes punctatus were investigated in Korea. The estimated allometric growth between the sexes showed significant differences in all morphometric measurements. In the classification of growth types, carapace width-chela length exhibited positive and negative allometric growth in males and females, respectively. Carapace width-abdominal width showed positive relative growth in both sexes, and orbital spine width exhibited negative relative growth in both sexes. Consequently, sexual dimorphism was evident in all measured traits. Growth parameters estimated using the ELEFAN function of the FiSAT II program indicated higher values in males compared to females. Asymptotic length (CW∞) for males was estimated at 139.2 mm, whereas for females it was 116.6 mm. Additionally, the growth coefficient (K) was higher in males (0.65) than in females (0.54), suggesting faster growth in males. The winter point (WP) was 1 for males and 0.7 for females, indicating slower growth in males during the colder December and slower growth in females during the spawning period in August. The modified von Bertalanffy growth curves indicated asymptotic growth in all sexes, and the growth performance index (φ') showed higher values in males (4.10) compared to females (3.87), reflecting differences in growth curves. The steady increase in recruitment rates from July to September was associated with the appearance of larvae and their subsequent growth into juveniles, leading to their recruitment into the population during this period. Therefore, O. punctatus exhibited sex-specific differences in growth parameters, suggesting distinct growth strategies between the sexes.


Approval for animal experiments
The Ovalipes punctatus used in this study does not require a permit for collection, and it is not currently considered an endangered or protected species in Korea.All experiments were conducted in accordance with the best practices to minimize animal suffering and followed the guidelines established by the Korean Association for Laboratory Animals in the Education on the Use and Management of Laboratory Animals.Also, all animal experiments conducted in this study were in compliance with the ARRIVE guidelines 26 .

Morphometric measurements
For the collected samples (males: 294, females: 183), carapace width, chela length, abdominal width, and orbital spine width were measured to the nearest 0.01 mm using a vernier caliper, and wet weight was measured to a resolution of 0.01 g using an electronic scale (CAS CUW6200H, Korea) (Fig. 2).For individuals with missing limbs when measuring wet weight, errors were minimized by measuring the weight of the intact legs and calculating the potential weight of the missing limbs, referring to the method of Zaleski and Tamone 27 .

Allometric growth analysis
The following formula was used to estimate the allometric growth for each morphometric measurement: Allometric growth of carapace width-body weight where BW is the body weight, CW is the carapace width, and a and b are constants.The constant b is the allometric growth coefficient; b < 3 indicates negative allometric growth (body weight increases slower than body length), b > 3 indicates positive allometric growth (weight increases faster than body length), and b = 3 indicates isometric growth 28 .Allometric growth of carapace width-chela length where CW is the carapace width, ChL is the chela length, and a and b are constants.Allometric growth of carapace width-orbital spine width where CW is the carapace width, OW is the orbital spine width, and a and b are constants.To classify the type of allometric growth of the morphometric measurement data, excluding weight data, we converted the existing linearized equation into the form Y = aX b , where Y is the dependent variable, and X is the independent variable.In the allometric growth analysis of most crabs, the carapace width is used as the independent variable X 29 .The classification of allometric growth types has been previously described 30 .b < 1 indicates negative allometric growth, where Y grows slower than X; b > 1 indicates positive allometric growth, where Y grows faster than X, and b = 1 indicates isometric growth.Sexual dimorphism between the sexes was tested using the Kolmogorov-Smirnov (K-S) test using the length-frequency distribution for each morphometric measurement.

Analysis of population characteristics
Mode separation of the cohort was performed after analyzing the average carapace width and standard deviation using Bhattacharya's method, and each mode was accurately represented using Hasselblad's normal separation (NORMSEP) method 31 .The reliability of the groups was determined using a separation index (S.I.).The recruitment pattern was estimated using the FiSAT II program.

Analysis of the modified von Bertalanffy growth function
The growth of O. punctatus was described using the modified von Bertalanffy growth function (VBGF), which represents the monthly carapace widths of females and males as a length-frequency distribution at 5 mm intervals: where CW t is the carapace width at age t, CW ∞ is the asymptotic carapace width, K is the intrinsic growth rate, t 0 is the theoretical age at zero length, C is the amplitude of seasonal growth oscillation, t s is the age at the beginning of growth oscillation, and winter point (WP; t s + 0.5) is the season of year when growth is the slowest.t 0 was estimated using Veiga's method 32 ; however, it was set to 0 because no results for the CW of the early larvae of O. punctatus were obtained.These growth parameters were estimated using ELEFAN in the FiSAT II program 33 , a non-parametric estimation method, and the reliability was expressed as the R n value.
The growth performance index between the sexes was analyzed and compared using the following formula 34 : where φ' is the growth performance index, CW ∞ is the asymptotic CW, and K is the intrinsic growth rate.

Data analysis
Differences in allometric growth between the sexes of O. punctatus were tested using analysis of covariance (ANCOVA).In all allometric growth graphs, the independent variable is carapace width, and the dependent variables are chela length, orbital spine width, and abdominal width.Additionally, statistical significance was determined using a t-test for the classification of allometric growth types.Kolmogorov-Smirnov test (K-S test) was performed to the analyze the length frequency distribution of the male and female individuals.Additionally, t-test was used to determine the statistical significance of the classification of allometric growth types, and the Kolmogorov-Smirnov test (K-S test) was performed to analyze the carapace width frequency distribution of males and females.All statistical analyses were performed using Microsoft Excel 2016 (Microsoft Corporation, Redmond, Washington, USA) and PAST 4.03 (PAleontological STatistics version 4.03) 35 .www.nature.com/scientificreports/

Classification of allometric growth types
The allometric growth types were classified by converting the existing linearized equation into the form Y = aX b (Table 1).The allometric growth types of the carapace width-chela length were ChL = 0.2626CW 1.0914 (R 2 = 0.9830, b > 0, n = 294) and ChL = 0.4245CW 0.9693 (R 2 = 0.9692, b < 0, n = 183) for males and females, respectively.Males showed positive allometric growth close to isometric growth, whereas females showed relatively negative allometric growth, which was close to isometric growth (t-test: p < 0.01).

Sex-specific carapace width frequency distribution
The carapace width frequency distribution of the O. punctatus showed a range of 42.3-132.5mm (mean ± SD: 89.7 ± 20.5 mm) for males and a range of 36.1-105.8mm (mean ± SD: 78.1 ± 14.0 mm) for females.The K-S test results for the male and female carapace width frequency distributions revealed a significant difference between the sexes (Z = 7.325, p < 0.001) (Fig. 4).

Mode analysis of Bhattacharya's method
The carapace width of the crabs per month was expressed as a length-frequency distribution, and mode separation was performed using Bhattacharya's method in the FiSAT II program (Fig. 5).During the research period from September to December, the distribution was separated into two modes, with S.I. values of 3.2, 4.4, 7.4, and 3.7, respectively.
The modes separated in each month were 63.1 ± 10.2 mm and 96.5 ± 10.9 mm in September; 57.6 ± 7.9 mm and 97.4 ± 10.3 mm in October; 81.9 ± 4.3 mm and 116.0 ± 4.9 mm in November; and 86.1 ± 5.5 mm and 112.4 ± 8.9 mm in December.www.nature.com/scientificreports/Growth equation estimation using the modified VBGF CW ∞ was estimated as 139.2 mm and 116.6 mm for males and females, respectively; thus, females were smaller than males (Fig. 6).K was 0.65 year −1 for males and 0.54 year −1 for females, thereby showing higher values for males.C was 0.1 for both sexes, and WP was 1 and 0.7 for males and females, respectively.Males had the slowest growth in December and females in August.The goodness of fit (R n ) of all growth parameters was 0.263 and 0.335 for males and females, respectively (Table 2).
The growth performance index (φ') was 4.10 and 3.87 for males and females, respectively, indicating that males grew faster than females.
At a 95% confidence level, the confidence interval (CI) for males was 18.42, with the upper limit and lower limit being 120.33 mm and 83.49mm, respectively.For females, the confidence interval (CI) was 15.49, with the upper limit and lower limit being 95.75 mm and 64.76 mm, respectively.

Recruitment patterns
After estimating the growth parameters (CW ∞ , K, C, and WP) using ELEFAN in the FiSAT II program, monthly recruitment patterns were estimated.The recruitment rate of O. punctatus did not exceed 10% from January to June; however, the rate increased to > 15% from July and reached the highest (21.1%) in September.Subsequently, the recruitment rate gradually decreased, showing a rapid decline from November (Fig. 7).

Discussion
The most frequently used measurement traits in crustacean growth studies are body weight, carapace length, and carapace width 36 .The maximum CW of male and female O. punctatus were 115.2 mm and 102.8 mm in Japan 22 , 63.8 mm and 63.2 mm in South Africa 37 , and 98 mm and 82 mm in China 23 , respectively.Sasaki and Kawasaki 22 reported male and female crabs with maximum CWs of 115.2 mm and 102.8 mm, respectively, whereas Wang et al. 23 reported widths of 98 mm and 82 mm, respectively.In the present study, the maximum CWs of O. punctatus in Korea were 132.5 mm and 105.8 mm for males and females, respectively, indicating that all sexes showed larger CWs than those reported in previous studies.
Growth refers to the increase in body volume resulting from the increase in body length and weight, and it can be divided into absolute growth, which represents the growth amount over time, and allometric growth, which describes the growth of other body parts relative to the increase in body length 38 .The allometric growth equation of body length and weight plays an important role in fisheries because it can estimate changes in body weight according to body length and can be used as an indicator of reproduction, feeding, and adaptability to the environment 4,39,40 .Males generally have larger sizes and weigh than females 41 .Mud crab Scylla olivacea (Herbst, 1796) (Brachyura: Portunidae) showed positive allometric growth in males and negative allometric growth in females 42 ; in snow crab Chionoecetes opilio (Fabricius, 1788) (Brachyura: Oregoniidae), males had a higher body weight than did females 43 .Ovalipes catharus (White in White & Doubleday, 1843) also exhibited a higher body weight in males compared to females 29 .Based on the carapace width-weight allometric growth results of this      study, males exhibited positive allometric growth (b = 3.14), while females showed negative allometric growth (b = 2.95).This difference is attributable to a sex-specific energy allocation strategy for crustaceans, in which males allocate more energy for body growth to gain an advantage in mating competition by increasing their body size, and females have smaller sizes and slower growth because they invest more energy in reproductive processes 5,44 .
In crabs, sexual dimorphism occurs primarily in the chelae, abdomen, and first pleopod, and the size of the specific part increases significantly upon molting 5 .The chelae of crabs are important for reproduction and social behavior 45 .Males have advantages in combat and courtship behavior because of sexual dimorphism in the chela 5 , and the chelae also play an important role in sexual appeal and mating during communication of sexual behavior, such as courtship 46 .In Johngarthia planata (Stimpson, 1860) of the family Gecarcinidae, the chelae of males are larger than those of females, and males show positive allometric growth 47 .A study on the allometric growth of Portunus pelagicus (Linnaeus, 1758) showed that the chelae of males were larger and showed positive allometric growth 48 .Du Preez and McLachlan 37 reported that O. punctatus males had longer chelae than females.In the present study, a significant difference was observed in the allometric growth of carapace width-chela length between the sexes.For the chela growth type, males showed positive allometric growth (b = 1.09) and females showed negative allometric growth (b = 0.96).Different types of chela growth are related to reproduction and spawning, and the presence of larger chelae in males is advantageous in mating competition 47 .
In the present study, R 2 was low (0.20) only for the allometric growth of abdominal width combined with both sexes because the abdominal width showed stronger sexual dimorphism than the other measured traits.In previous studies of the genus Ovalipes, allometric growth of abdominal width was more common in females than in males, and all females showed strong positive allometric growth 29,37,49 .In the present study, there was a significant difference in the allometric growth of carapace width-abdominal width between the sexes, and sexual dimorphism was observed in the frequency distribution of abdominal width.In addition, for growth type, the b-value of all sexes was greater than 1, indicating positive allometric growth.The b-value of females was 1.63, indicating strong positive allometric growth.Additionally, in the study by Davidson and Marsden 29 , the abdominal growth of female O. catharus, a species in the same genus, exhibited two growth phases, primarily occurring around a carapace width of 30 − 40 mm.This phenomenon, often seen in many decapods, is associated with the pubertal molt, which results in a marked increase in the slope of the allometric growth graph.In our study, while the O. punctatus did not show a clear separation, there was a slight change in the slope between the 40-50 mm carapace width range on the graph.However, to accurately determine the pubertal molt interval and its relationship with sexual maturity in O. punctatus, further collection of smaller specimens and integration with reproductive ecological research is required.
Crabs can be divided into two groups (narrow and wide) based on the distance between the eyes.O. punctatus belongs to a group of species with a wide width, and species in this group can recognize the exact distance of an object in a three-dimensional space because their visual fields overlap significantly.This is advantageous for searching for prey and recognizing predators, thereby increasing survival rates 50 .In the present study, there was a significant difference in the allometric growth of the carapace width-orbital spine width between the sexes.Moreover, sexual dimorphism was observed in the frequency distribution of orbital spine width, and the growth type showed negative allometric growth in all sexes (b < 1).This negative allometric growth of the orbital spine width is a phenomenon that also occurs in most crabs.This phenomenon restricts the growth of the anterior part of the carapace such that it grows slower than the rest of the carapace because a blind spot may occur if the gap is extremely wide 51 .
Crustaceans do not exhibit age traits, and their growth has been studied using the length-frequency method 38 .In the NORMSEP results, two modes appeared from September to December, and the S.I. of each mode was > 2, indicating that the age groups were well separated.The high S.I. in the results is considered that the number of modes in the frequency distribution of body length was clearly shown.Because the variance in body length for each age was small, as O. punctatus individuals have short lifespans and are fast-growing 52 .However, research on crab growth presents difficulties in interpreting data because collecting juvenile crabs is unfeasible in the early stages of settlement 53 .Therefore, collecting samples according to body length is necessary for the collection of various crab stages to accurately separate the age groups and estimate the lifespan of crabs.
Crustacean growth exhibits an asymptotic pattern owing to molting and seasonal influences 41 .These asymptotic patterns are short and discontinuous because crustaceans grow by molting.The VBGF in this study used a modified growth equation that considered seasonal fluctuation factors and molting, which is different from the existing growth equations, as shown in the resulting graph.
The estimated growth parameters (CW ∞ , K, C, and WP) were 139.2 mm, 0.65 year −1 , 0.1, and 1 and 116.6 mm, 0.54 year −1 , 0.1, and 0.7 for males and females, respectively.Thus, the CW ∞ and K of O. punctatus were larger in males than in females 54 , which is the same pattern as the parameter estimation growth results for Portunus segnis (Forskål, 1775) 55 , Portunus trituberculatus in the East China Sea 56 , and P. trituberculatus in the Yellow Sea 57 .The difference in variables between the sexes is assumed to be caused by the differences in reproductive strategies, in which males gain an advantage in mating behavior by focusing on body growth, whereas females use more energy to develop internal reproductive organs.The seasonal growth oscillation (C) estimated by the growth curve was 0.1 for both sexes, indicating that O. punctatus showed marginal seasonal oscillation in growth.The period for slowest growth (WP) was December (1) for males and August (0.7) for females.These results are attributable to low water temperature in winter, which affects the growth of males, and August is the spawning season for females.These growth characteristics were also observed in the intertidal mud crab, Macrophthalmus japonicus (De Haan, 1835) 58 .
The growth performance index (φ') is useful for comparing growth under various environmental conditions 57 .This index was higher in O. punctatus males than in females because females invest more energy in the maturation of gonads than in body growth, and they suppress feeding, which causes low growth rates and prevents or delays www.nature.com/scientificreports/molting 59 .Similarly, the finding that males grow faster than females has also been observed in the orange mud crab, Scylla olivacea, which belongs to the same superfamily, Portunoidea 42 .However, in the case of the swimming crab, Portunus trituberculatus, which also belongs to the same superfamily, females were found to grow faster than males 54 .Such sex-specific growth differences among decapod species are common and have been recorded in various previous studies 59 .
The results indicated that the recruitment pattern of O. punctatus aligned with that of Portunus trituberculatus, which has a similar spawning season and inhabits the same Yellow Sea 54 .According to Lee et al. 60 , the larvae of O. punctatus in Korea appear from April to June, and the larvae released from ovigerous females grow into juveniles approximately 30 days later 61 .The continuous increase in recruitment rates from July to September observed in this study is associated with the appearance of larvae and their subsequent growth into juveniles, leading to their recruitment into the population during this period.
In crustacean studies, estimating growth parameters and applying mathematical models to arrive at von Bertalanffy growth function and population cohorts provides reliable estimates of crustacean species 41 .In addition, studying growth and population characteristics using estimates enables the interpretation of population dynamics and potential resource management 1 .In the results, the VBGF graphs for each sex of O. punctatus already showed significant differences from the 0 to 1 year age interval and the goodness of fit (R n ) was above 0.2, indicating suitability.However, previous studies on Portunus sanguinolentus (Herbst, 1783) and P. trituberculatus, which belong to the same superfamily Portunoidea, did not show clear differences between the sexes in the VBGF graphs 54,62 .This can be easily explained by the growth performance index (φ'), which is a much more appropriate and robust method for comparing crustacean growth than simply comparing CW ∞ and K values 59 .According to the results of Oh 54 , the growth performance indices of P. trituberculatus were 2.48 for males and 2.51 for females, whereas in this study, the values for O. punctatus were 4.10 for males and 3.87 for females, highlighting a stark contrast.These differences in crustacean growth may be due to environmental factors such as sea temperature 62 , indicating a need for future investigations into the correlations with marine environmental factors.Therefore, it can be concluded that not all species within the superfamily Portunoidea exhibit differences in growth curve patterns between sexes.
In Asian countries, ongoing overfishing of O. punctatus has led to a decrease in individual size, highlighting the need for institutional resource management policies based on ecological research findings 23 .Therefore, to protect the population of O. punctatus and enable sustainable fisheries, it is essential to establish resource management policies such as closed seasons and minimum size limits based on ecological data.Future reproductive ecological studies combined with the sex-specific growth characteristics estimated in this study can provide strengthened data to serve as a basis for policy formulation.

Fig. 1 .
Fig. 1.Sampling area of sand crab Ovalipes punctatus in coastal waters of Korea in 2021.

Fig. 4 .
Fig. 4. Length frequency distribution of sand crab Ovalipes punctatus in the Yellow Sea of Korea in 2021.M males, F females.

Fig. 5 .
Fig. 5. Monthly modes separation of length-frequency distribution and normal distribution curves of sand crab Ovalipes punctatus using NORMSEP.

Fig. 6 .
Fig. 6.The modified von Bertalanffy growth curves for males and females of sand crab Ovalipes punctatus based on length-frequency distributions.CW ∞ are represented by the black dashed line.M males, F females.

Table 1 .
Allometric growth equations and growth type of sand crab Ovalipes punctatus in the Yellow Sea of Korea in 2021.+ Positive allometric growth, -Negative allometric growth, CW carapace width, ChL chela length, AW abdominal width, OW orbital spine width.

Table 2 .
Modified von Bertalanffy growth parameter estimation using ELEFAN analysis of length-frequency data for males and females.CW ∞ asymptotic length (mm), K growth coefficient (yr −1 ), t 0 theoretical age at zero length (years), C amplitude of growth oscillation, WP winter point, φ' growth performance index, R n score function.